AC=ABsinB=2√5*(√5/5)=2

BC^2=AB^2-AC^2=20-4= 16

BC=4

(2)△ABC is similar to △DPC, and PC:BC=DC:AC.

PC*AC=BC*DC

2x=4DC

x=2DC

△ The area of △ADP is Y=PC*AD/2=x(AC-DC)/2=x(2-DC)/2.

2Y=x(2-DC)

4Y=x(4-2DC)=x(4-x)

y=x-x^2/4=-( 1-x/2)^2+ 1

When x=2, y max = 1.